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Riemannsche Zahlensphäre Und Möbius-Transformationen

Riemannsche Zahlensphäre Und Möbius-Transformationen

          
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About the Book

In diesem Buch wird der Punkt Unendlich zum Greifen nahe! Mit seiner berühmten Zahlenkugel fand Riemann eine Darstellung, in die der "unendlich ferne Punkt" völlig gleichberechtigt zu den Punkten steht, die durch endliche Zahlenwerte beschrieben werden. Neben der Konstruktionsanleitung dieser Kugel widmen wir uns ausführlich den topologischen Grundlagen von ℂ=ℂ∪{∞} und den Eigenschaften der stereographischen Projektion. Zudem wird der Bezug zu einem wichtigen Abbildungstypen der Funktionentheorie hergestellt: den Möbius-Transformationen. Möbius-Transformationen bilden die Automorphismen von C und kommen beispielsweise in der speziellen Relativitätstheorie und der Elektrotechnik ("Smith-Diagramm") zur Anwendung.

Die als Lehrskript verfasste Lektüre umfasst das Fundament für das Verständnis beider Themen und beleuchtet ihre Verbindung. Sie enthält den ausführlich ausgearbeiteten Beweis zum berühmten YouTube-Video "Möbius Transformations Revealed" (2008) von Arnold und Rogness und richtet sich an Interessierte der Mathematik, die bereits mit den Grundlagen der reellen Analysis, linearen Algebra und Differentialgeometrie vertraut sind.

Der Autor

Maximilian Wiecha studierte an der TU Braunschweig Chemie und Mathematik auf gymnasiales Lehramt. Im Laufe seines Studiums vertiefte er beide Fachrichtungen und beschäftigte sich u. a. mit der selektiven Synthese unsymmetrischer Diboran(IV)-Derivate. Neben seiner Leidenschaft für anorganische und physikalische Chemie, gehören die höhere Mathematik. Sein Interesse liegt auf Forschung und universitärer Lehre.


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Product Details
  • ISBN-13: 9783662694206
  • Publisher: Springer
  • Publisher Imprint: Springer Spektrum
  • Language: German
  • Returnable: Y
  • ISBN-10: 3662694204
  • Publisher Date: 10 Oct 2024
  • Binding: Paperback
  • No of Pages: 149


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